I have two suggestions based on experience, both of which involve taking a train out of Nice.
There's a fabulous train going out of the main station towards Torino through the Bas Alpes. Sospel is a small town with some accommodation, lots of riding & waking around. There are other towns with stations along the way, some of which are fabulous. Breil & Tende may be on the line.

Edit: the train has half-carriages set out for carrying bikes. There will be bags of space if you're planning to ride there.

There's a narrow-guage railway running from a separate station, going NW through some lovely countryside. Entrevaux is a tine town which might suit you. Check them all out.

Grasse is 1/2 hr drive and is a nice ( slightly touristy) town, quiet in the evening, further afield Fayance is smaller and quieter still with a lovely small French market town feel to it. Both within easy drive of Nice

Beaulieu-sur-mer is lovely, we stayed there on honeymoon a few years ago. Just round the coast on the train from Nice. Some great driving roads especially the one over the hills to Monaco, the weather was so hot our mx5 was cooler with the roof up!

Menton for me ,I,ve been 3 times or Cap de Ferrat if the budget allows ,we rented a Penthouse in Cap de Ferrat such a nice quite place ?Menton is a much cheaper alt to Monaco only 15 mins drive away and right on the ocean?

Got a soft spot for Bandol - great little town on the coast .
Must be something to do with nipping into the bank just before lunch to be served by what can only be described as a goddess and seeing her 10 minutes later - sans attire on the (quiet) beach ....